(1) Application Field of the Invention
This invention relates to a method which compresses and reproduce digital data signals such as digital audio signals, digital video signals and digital numerical signals, more particularly to a method which converts digital data binary signals with 2 as base to corresponding compressed digital data signals consisting of numbers of two digit binary system and reproduces them Further, this invention relates to a method which uniquely converts digital data signals of binary numbers with 2 as base to those of ternary numbers with 3 as base, and vice versa. Furthermore, this invention relates to a method which uniquely converts the above-described digital numerical signals to notations which can prevent chain of carry digits to shorten the operation time, when making arithmetical operation using the digital numerical signals, and a method which can shorten operational time using a table of parameters depending on divisor and dividend or a combination of partial dividends, when making divisional calculations, as well as a digital signals and data converter and a digital computer using the above methods.
(2) Description of Prior Art
As well known, with most of the digital data signal processors according to the prior art, digital data signals are processed using numbers of the two digit binary system consisting of two signals {0, 13}. These digital data signals are kept in memory. The digital data signals of two digit binary numbers are also used to send and receive digital data signals by way of communications between other units.
With most of digital signals and data converters and digital computers, numbers of two digit binary system using signal set {0, 1} are processed, and also the calculation results in numbers of the same system. To shorten the operational time, numbers of redundant binary system using three signals {-1, 0, 1} at one digit have been utilized.
In most cases, digital data signals such as digital audio signals, digital video signals and digital numerical signals are handled as a fixed length by the characteristics of their respective signals. For example, when transferring digital numerical signals, if they have a 16 bit fixed length, the same 16 bits are used even to a zero signal which can be expressed by using only one bit. This is because of the following fact: when a cluster of two or more digital data signals is transferred, it is easy to divide each of them into two sets of 16 bits by clearly indicating only the boundary of the starting portion and the end portion, even without specification of the partitions of the individual digital data signals. Further, when digital data signals with various bit numbers are mixed, an indication of the respective bit numbers with variable length having different bit numbers for every digital data signal will need 4 bits to express numbers of 1 to 16 bits, therefore, as a whole, causing the size of individual data signals becoming 5 to 20 bits, thus resulting in an average of bit numbers being larger than 16 bits, that means of no use in reducing bit numbers. Furthermore, in the case of digital video signals, they have less mixing of signals with various bit numbers and more signals using the whole of assigned bit numbers, thus resulting in a rare happening of shorter variable length than fixed length.
Therefore, in spite of the fact that a reduction of the total number of digits as a cluster of data signals can not only minimize necessary memory area, but also make transfer time shorter when loading them on communication means, the aforementioned numbers of two digit binary system cannot reduce the quantity of digital data signals because of their non-redundancy and a possible increase taking place in the quantity of them due to their originally simplest configuration when any slightest signals are added, so that how to compress digital data signals have been a significant problem.
On the other hand, when expressing one numerical value, because of the redundancy which may accommodate a plurality of notations, the aforementioned numbers of three digit binary system may shorten operational time if a notation which may not take place carry digit when making addition, subtraction and multiplication calculations should be selected. But, some contents of two numbers to be processed may necessitate to select alternative notations to each other, thus resulting in a complexity in the conversion process of their numerical signals. Additionally, in the case of divisional calculations, because of the redundancy, only a comparison of digit numbers cannot determine even which numerical value is larger than the other, therefore causing a difficulty in divisional calculation, thus resulting in the need for the solution.
Further, when handling numbers of 3-based ternary system as digital data signal, the conversion between them and numbers of 2-based binary system may be easy when they are integers, but in the case of decimals, one system may be divided out but the other system may often result in recurring decimals, thus causing a difficulty in unique conversion.
Since the divisional calculation takes the longest calculation time among the four rule calculations, an issue was how to reduce the time necessary for the divisional calculation. Such a device has been developed as to make a calculation for determining a reciprocal of a divisor only by a combination of addition, subtruction and multiplication calculations.